Let€™s use the Sampling Distribution of the Sample Mean web app accessible from the book€™s website to show that the first population distribution shown in Figure 7.11 has a more nearly normal sampling distribution for the mean as n increases. Select uniform for the population distribution and keep the default settings of 0 and 1 for the lower and upper bound.

a. Use the app to simulate the sampling distribution when the sample size n = 2. Run 10,000 simulations and look at the resulting histogram of the sample means. (You may want to decrease the binsize a bit to get a clearer picture.) What shape does the simulated sampling distribution have?
b. Repeat part a, but now use a sample size of n = 5. Explain how the variability and the shape of the simulated sampling distribution changes as n increases from 2 to 5.
c. Repeat part a, but now use a sample size of n = 30. Explain how the variability and the shape of the simulated sampling distribution changes as n increases from 2 to 30. Compare results from parts a-c to the first column of Figure 7.11.
d. Explain how the central limit theorem describes what you have observed.

Transcribed Image Text:

Population Distributions мL a La M. For this population, the sampling distribution for n = 2 is triangular. Sampling Distributions of I n = 2 Д, А, , LA, Д. п 5 n = 30